This information may be on the deeds or referred to in a local history book.
If this information is not available, or you just want an approximate date, unless there is a date mark on the house or a similar neighbour, you will have to resort to the style of the building.
The most reliable method for dating a house is to use street directories, usually available at local history departments of local libraries.
By looking for the first reference to the building, perhaps even 'Vacant', you can prove that the house existed by that year. Beware of the compilation dates of each of these sources.
Sites on the list are generally from the First Period of American architecture or earlier. Oldest church building in the US and its territories, originally built in its current location (extensive additions and renovations).